Also find the Eigenvalues of B Problem 2 Compute the determinant of 1 0 0 B...
Problem 2: Let 4 1 2 5 1-1 0 3 2 0 3 2 a) Find the eigenvalues, eigenspaces of the linear operators LB, Lo. b) Using part a), find a basis for R3 that diagonalizes the linear operators c) Write B- EDE- with D a diagonal matrix. d) Find the eigenvalues, eigenspaces, and generalized eigenspaces of LA Problem 2: Let 4 1 2 5 1-1 0 3 2 0 3 2 a) Find the eigenvalues, eigenspaces of the linear...
Problem 3 Find the determinant of the following matrix: -2 6 0 1 0 -12 10 0
Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3 Problem 8. (15 points) Find eigenvalues and eigenvectors of the follwing matrix 3 -2 0 A= -1 3-2 0 -1 3
Question 1: Given the following matrix A. 02 A- 1 2 3 2 (a) Find the determinant of A (b) Find eigenvalues and the corresponding eigenspaces of A (c) Determine whether A is diagonalizable. If so, find a matrix P and a diagonal matrix D such that P-1AP=D If not, justify your answer. (d) Find a basis of Im(A) and find the rank of Im(A) (e) Find a basis of Ker(A) and find the rank of Ker(A) Question 1: Given...
Find the terms of the determinant associated with the permutations 2,3,1,4 and 3,1,4,2 Compute the determinant? 1 [? ? 0 1 -1 0 3 -1 3 0 ? 0 4 ?
Problem 2. For the following system, (a) compute the eigenvalues, (b) compute the associated eigenvectors, (c) if the eigenvalues are complex, determine if the origin is a spiral sink, a spiral source, or a center; determine the natural period and natural frequency of the oscillations, and determine the direction of the oscillations in the phase plane, (d) sketch the phase portrait for the system; and (e) compute the general solution dY (1 -2
1. 4 2 0 A-1 1 1 0 0 3 (a) Find the characteristic polynomial of A. (b) What are A's eigenvalues? (c) Find the corresponding eigenvectors (d) Is A diagonalizable? Why or why not. 84 1. 4 2 0 A-1 1 1 0 0 3 (a) Find the characteristic polynomial of A. (b) What are A's eigenvalues? (c) Find the corresponding eigenvectors (d) Is A diagonalizable? Why or why not. 84
Problem 8. a) Find the determinant det (A) for the matrix [1 -3 41 A 2 0 -1 1 b) Decide whether the matrix A has an inverse. If the inverse matrix A-1 exists, find its determinant det(A-1).
3. This problem defines A = 2 6 (a) Find the eigenvalues of A. (b) Find an eigenvector for each eigenvalue. (c) Find a diagonalization of A. For the following matrices, write out a general solution of y' use complex or real forms as you prefer. Ay using eigenanalysis. You may 4. A=12 3 0-1 5. A =1-20 6 6. A=1-4-2
(1 point) Compute the determinant of the matrix -1 -2 -4 -6 -7 -7 7 7 A= 0 0 0 0 -4 -5 7 det(A) (1 point) Find the determinant of the matrix 6 A- 6 -9 -7 det(A) (1 point) Find the determinant of the matrix 2 2 -2 B= 1 -1 2 3 -2 det (B)